Sturm-Liouville 方程节点的锐界

Monatshefte für Mathematik Pub Date : 2024-01-30 DOI:10.1007/s00605-023-01940-0

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引用次数: 0

摘要

摘要 Sturm-Liouville 问题的节点是特征函数的内部零点。本文的目的是在给定势的$L^1$ 准则时，对具有 Dirichlet 边界条件的 Sturm-Liouville 方程的节点锐界结果提出一个简单而新颖的证明。基于外近似方法，我们将把这个无穷维优化问题简化为有限维优化问题。

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Sharp bounds of nodes for Sturm–Liouville equations

Abstract

A node of a Sturm–Liouville problem is an interior zero of an eigenfunction. The aim of this paper is to present a simple and new proof of the result on sharp bounds of the node for the Sturm–Liouville equation with the Dirichlet boundary condition when the $L^1$ norm of potentials is given. Based on the outer approximation method, we will reduce this infinite-dimensional optimization problem to the finite-dimensional optimization problem.

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Monatshefte für Mathematik

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